Solve sqrt{(60/3.6)^2-{2*0,8*9,81*(16,2-60/3,6*0,8)}}

$$\sqrt { ( \frac { 60 } { 3.6 } ) ^ { 2 } - \{ 2 \times 0,8 \times 9,81 \times ( 16,2 - \frac { 60 } { 3,6 } \times 0,8 ) \} }$$

Evaluate

$$\frac{\sqrt{1309402}}{75}\approx 15.257213959$$

Solution Steps

Expand \frac{60}{3.6} by multiplying both numerator and the denominator by 10.

$$\sqrt{\left(\frac{600}{36}\right)^{2}-2\times 0.8\times 9.81\left(16.2-\frac{60}{3.6}\times 0.8\right)}$$

Reduce the fraction \frac{600}{36} to lowest terms by extracting and canceling out 12.

$$\sqrt{\left(\frac{50}{3}\right)^{2}-2\times 0.8\times 9.81\left(16.2-\frac{60}{3.6}\times 0.8\right)}$$

Calculate \frac{50}{3} to the power of 2 and get \frac{2500}{9}.

$$\sqrt{\frac{2500}{9}-2\times 0.8\times 9.81\left(16.2-\frac{60}{3.6}\times 0.8\right)}$$

Multiply 2 and 0.8 to get 1.6.

$$\sqrt{\frac{2500}{9}-1.6\times 9.81\left(16.2-\frac{60}{3.6}\times 0.8\right)}$$

Multiply 1.6 and 9.81 to get 15.696.

$$\sqrt{\frac{2500}{9}-15.696\left(16.2-\frac{60}{3.6}\times 0.8\right)}$$

Expand \frac{60}{3.6} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{2500}{9}-15.696\left(16.2-\frac{600}{36}\times 0.8\right)}$$

Reduce the fraction \frac{600}{36} to lowest terms by extracting and canceling out 12.

$$\sqrt{\frac{2500}{9}-15.696\left(16.2-\frac{50}{3}\times 0.8\right)}$$

Multiply \frac{50}{3} and 0.8 to get \frac{40}{3}.

$$\sqrt{\frac{2500}{9}-15.696\left(16.2-\frac{40}{3}\right)}$$

Subtract \frac{40}{3} from 16.2 to get \frac{43}{15}.

$$\sqrt{\frac{2500}{9}-15.696\times \frac{43}{15}}$$

Multiply 15.696 and \frac{43}{15} to get \frac{28122}{625}.

$$\sqrt{\frac{2500}{9}-\frac{28122}{625}}$$

Subtract \frac{28122}{625} from \frac{2500}{9} to get \frac{1309402}{5625}.

$$\sqrt{\frac{1309402}{5625}}$$

Rewrite the square root of the division \sqrt{\frac{1309402}{5625}} as the division of square roots \frac{\sqrt{1309402}}{\sqrt{5625}}.

$$\frac{\sqrt{1309402}}{\sqrt{5625}}$$

Calculate the square root of 5625 and get 75.

$$\frac{\sqrt{1309402}}{75}$$